To find the mixed number equivalent of the fraction [tex]\(\frac{57}{13}\)[/tex], follow these steps:
1. Divide the numerator by the denominator:
Calculate the quotient and the remainder when 57 is divided by 13.
- The quotient represents the whole number part of the mixed number.
- The remainder represents the numerator of the fractional part.
2. Perform the division:
- [tex]\(57 \div 13 = 4\)[/tex] with a remainder.
- To find the remainder: [tex]\(57 - (13 \times 4) = 57 - 52 = 5\)[/tex].
3. Form the mixed number:
- The quotient from the division (4) is the whole number part.
- The remainder (5) is the numerator of the fractional part, and the denominator remains the same (13).
Thus, [tex]\(\frac{57}{13}\)[/tex] can be written as the mixed number [tex]\(4 \frac{5}{13}\)[/tex].
4. Compare the options:
- The mixed number we found, [tex]\(4 \frac{5}{13}\)[/tex], matches the fourth option.
So, the correct option is:
[tex]\[ \boxed{4 \frac{5}{13}} \][/tex]
